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Quadratic Expresions - Complete Squares
Adding and Subtracting Fractions with Like Denominators
Multiplying a Fraction by a Whole Number
Solving Equations with Log Terms and Other Terms
Solving Quadratic Equations by Factoring
Locating the Solutions of the Quadratic Equation
Properties of Exponents
Solving Equations with Log Terms on Each Side
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Graphs of Trigonometric Functions
Estimating Products and Quotients of Mixed Numbers
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Adding Polynomials
Adding Fractions with Unlike Denominators
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Dividing With Fractions
Multiplication Property of Equality
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Solving Proportions Using Cross Multiplication
Using the Quadratic Formula
Scientific Notation
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Graphing Equations in Three Variables
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Adding and Subtracting Fractions
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Rise and Run
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Solving Systems of Linear Inequalities
Multiplication Property of Radicals
A Quadratic within a Quadratic
Graphing a Linear Equation
Calculations with Hundreds and Thousands
Multiplication Property of Square and Cube  Roots
Solving Equations with One Log Term
The Cartesian Coordinate Plane
Equivalent Fractions
Adding and Subtracting Square Roots
Solving Systems of Equations
Exponent Laws
Solving Quadratic Equations
Factoring Trinomials
Solving a System of Three Linear Equations by Elimination
Factoring Expressions
Adding and Subtracting Fractions
The parabola
Computations with Scientific Notation
Quadratic Equations
Finding the Greatest Common Factor
Introduction to Fractions
Simplifying Radical Expressions Containing One Term
Polynomial Equations
Graphing and Intercepts
The Number Line
Adding and Subtracting Rational Expressions with Different Denominators
Scientific Notation vs Standard Notation
Powers
Factoring by Grouping
Extraneous Roots
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Linera Equations
Integers and Substitutions
Squares and Square Roots
Adding and Subtracting Rational Expressions with Different Denominators
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Expansion of a Product of Binomials
Powers and Exponents
Finding The Greatest Common Factor
Quadratic Functions
The Intercepts of a Parabola
Solving Equations Containing Rational Expressions
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Subtracting Polynomials
Solving Equations
Adding Fractions with Unlike Denominators
Solving Systems of Equations by Substitution
Solving Equations
Product and Quotient of Functions
   
 

Subtracting Polynomials

If you know how to add polynomials, then you already know how to subtract them. You just need to add the opposite of the polynomial that follows the minus sign. Take a look at the following examples.

a) (-2c2 +10c -9) - (5c2 -8c + 2) Watch the signs.
= (-2c2 +10c -9) + (-1)(5c2 -8c + 2) Change to (-1) times polynomial.
= (-2c2 +10c -9) + (-5c2 +8c - 2) Distribute the (-1) over the 2nd polynomial.
= [(-2c2 ) +(-5c2 )] + (10c + 8c) +[(-9) + (- 2)] Apply associative and commutative properties.
= ( -7c2  + 18c -11) Add coefficients.

 

b) (9x3 - 3x2 -7) - (-6x3 + 4x + 9) Note that the middle terms aren’t “similar”.
= (9x3 - 3x2 -7) +(-1)(-6x3 + 4x + 9) Watch the signs. Change to (-1) times polynomial.
= (9x3 - 3x2 -7) +(+6x3 - 4x - 9) Distribute the (-1) over the 2nd polynomial.
= (9x3 + 6x3 ) +(-3x2 ) +(- 4x) + (-7 - 9) Apply the associative and commutative properties.
= (9 + 6)x3 + (-3)x2  - 4x + (-7 - 9) Apply the distributive property.
= 15x3 - 3x2  - 4x - 16 Add coefficients.
 
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